Graphing - Parallel and Perpendicular Lines

If you have two lines on a graph, and you have determined their equations or slopes, you may be asked if the two lines are parallel or perpendicular to each other.

Parallel lines are at the same angle and will never cross... like two railroad tracks. It doesn't matter what direction the lines travel. As long as they are going the same way, they are parallel. In mathematical terms, two lines are said to be parallel if they have the exact same slope.

So, y = 3x + 5 and y = 3x + 200 are parallel lines (they differ in their y-intercepts, but they have the same slope m).

Perpendicular lines have a bit of a twist to them. Two lines are perpendicular if they cross (remember, any two straight lines that are NOT parallel will cross at a single point) and they form a 90 degree angle. eg. The x-axis and y-axis are perpendicular to each other. Mathematically, if line 1 has a sl! ope of m1, then a perpendicular line 2 will have a slope m2=(-1/m1)... that is, it's slope will be the negative inverse of the first.

Try it out... y=2x + 1 and y= (-1/2)x +5... m1=2 and m2=(-1/2). Check it out on the graph to see that they indeed form a 90 degree angle where they intersect.

To determine if lines are parallel or perpendicular, all you need to know is their slopes!

find the slope and y intercept